Define domain and intervals of rising/falling

"Define domain and intervals of rising/falling of the following function f(x): ."

Domain of is where :

What about function falling/rising (assuming that I got the domain right)? Isn't it so, that you just take derivative of f(x) and that "cancels" the integral, which would mean that f(x) is always rising for , because its derivative ( ) is always positive with ?

"Define domain and intervals of rising/falling of the following function f(x): ."

Domain of is where :

What about function falling/rising (assuming that I got the domain right)? Isn't it so, that you just take derivative of f(x) and that "cancels" the integral, which would mean that f(x) is always rising for , because its derivative ( ) is always positive with ?

f(x) is 'rising' for values of x such that f'(x) > 0 and 'falling' for values of x such that f'(x) < 0.